Abstract
We study the Casimir energy of bulk fields in AdS3 and its relation to subleading terms in the central charge of the dual CFT2. Computing both sides of the standard CFT2 relation E = −c/12 independently we show that this relation is not necessarily satisfied at the level of individual bulk supergravity states, but in theories with sufficient supersymmetry it is restored at the level of bulk supermultiplets. Assuming only (0, 2) supersymmetry (or more), we improve the situation by relating quantum corrections to the central charge and the supersymmetric Casimir energy which in turn is related to an index. These relations adapt recent progress on the AdS5/CFT4 correspondence to AdS3/CFT2 holography. We test our formula successfully in several examples, including the (0, 4) MSW theory describing classes of 4D black holes and the large (4, 4) theory that is interesting for higher spin holography. We also make predictions for the subleading central charges in several recently proposed (2, 2) dualities where the CFT2 is not yet well-understood.
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References
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP07 (1998) 023 [hep-th/9806087] [INSPIRE].
A. Bilal and C.-S. Chu, A note on the chiral anomaly in the AdS/CFT correspondence and 1/N 2correction, Nucl. Phys.B 562 (1999) 181 [hep-th/9907106] [INSPIRE].
P. Mansfield and D. Nolland, Order 1/N 2test of the Maldacena conjecture: cancellation of the one loop Weyl anomaly, Phys. Lett.B 495 (2000) 435 [hep-th/0005224] [INSPIRE].
P. Mansfield, D. Nolland and T. Ueno, Order 1/N 2test of the Maldacena conjecture 2. The full bulk one loop contribution to the boundary Weyl anomaly, Phys. Lett.B 565 (2003) 207 [hep-th/0208135] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, The spectrum of IIB supergravity on AdS 5 × S 5/Z 3and a 1/N 2test of AdS/CFT, JHEP06 (2013) 024 [arXiv:1304.1540] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, 1/N 2corrections to the holographic Weyl anomaly, JHEP01 (2014) 002 [arXiv:1310.2611] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, c − a from the N = 1 superconformal index, JHEP12 (2014) 145 [arXiv:1407.6024] [INSPIRE].
M. Beccaria and A.A. Tseytlin, Higher spins in AdS 5at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT, JHEP11 (2014) 114 [arXiv:1410.3273] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, Central charges from the N = 1 superconformal index, Phys. Rev. Lett.114 (2015) 091603 [arXiv:1411.5028] [INSPIRE].
M. Beccaria, G. Macorini and A.A. Tseytlin, Supergravity one-loop corrections on AdS 7and AdS 3, higher spins and AdS/CFT, Nucl. Phys.B 892 (2015) 211 [arXiv:1412.0489] [INSPIRE].
H.-C. Kim and S. Kim, M5-branes from gauge theories on the 5-sphere, JHEP05 (2013) 144 [arXiv:1206.6339] [INSPIRE].
H.-C. Kim, S. Kim, S.-S. Kim and K. Lee, The general M5-brane superconformal index, arXiv:1307.7660 [INSPIRE].
B. Assel, D. Cassani and D. Martelli, Localization on Hopf surfaces, JHEP08 (2014) 123 [arXiv:1405.5144] [INSPIRE].
A. Arabi Ardehali, J.T. Liu and P. Szepietowski, High-temperature expansion of supersymmetric partition functions, JHEP07 (2015) 113 [arXiv:1502.07737] [INSPIRE].
B. Assel, D. Cassani, L. Di Pietro, Z. Komargodski, J. Lorenzen and D. Martelli, The Casimir energy in curved space and its supersymmetric counterpart, JHEP07 (2015) 043 [arXiv:1503.05537] [INSPIRE].
N. Bobev, M. Bullimore and H.-C. Kim, Supersymmetric Casimir energy and the anomaly polynomial, JHEP09 (2015) 142 [arXiv:1507.08553] [INSPIRE].
H.W.J. Bloete, J.L. Cardy and M.P. Nightingale, Conformal invariance, the central charge and universal finite size amplitudes at criticality, Phys. Rev. Lett.56 (1986) 742 [INSPIRE].
I. Affleck, Universal term in the free energy at a critical point and the conformal anomaly, Phys. Rev. Lett.56 (1986) 746 [INSPIRE].
P. Kraus and F. Larsen, Microscopic black hole entropy in theories with higher derivatives, JHEP09 (2005) 034 [hep-th/0506176] [INSPIRE].
J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys.104 (1986) 207 [INSPIRE].
S. Giombi and I.R. Klebanov, One loop tests of higher spin AdS/CFT, JHEP12 (2013) 068 [arXiv:1308.2337] [INSPIRE].
R.R. Metsaev, Massless mixed symmetry bosonic free fields in d-dimensional anti-de Sitter space-time, Phys. Lett.B 354 (1995) 78 [INSPIRE].
J. de Boer, A. Pasquinucci and K. Skenderis, AdS/CFT dualities involving large 2D N = 4 superconformal symmetry, Adv. Theor. Math. Phys.3 (1999) 577 [hep-th/9904073] [INSPIRE].
M. Baggio, O. Ohlsson Sax, A. Sfondrini, B. Stefanski and A. Torrielli, Protected string spectrum in AdS 3/CFT 2from worldsheet integrability, JHEP04 (2017) 091 [arXiv:1701.03501] [INSPIRE].
L. Eberhardt, M.R. Gaberdiel, R. Gopakumar and W. Li, BPS spectrum on AdS 3 × S 3 × S 3 × S 1, JHEP03 (2017) 124 [arXiv:1701.03552] [INSPIRE].
P. Benetti Genolini, D. Cassani, D. Martelli and J. Sparks, The holographic supersymmetric Casimir energy, Phys. Rev.D 95 (2017) 021902 [arXiv:1606.02724] [INSPIRE].
P. Benetti Genolini, D. Cassani, D. Martelli and J. Sparks, Holographic renormalization and supersymmetry, JHEP02 (2017) 132 [arXiv:1612.06761] [INSPIRE].
G. Plunien, B. Müller and W. Greiner, The Casimir effect, Phys. Rept.134 (1986) 87 [INSPIRE].
G. Plunien, B. Muller and W. Greiner, Casimir energy at finite temperature, PhysicaA 145 (1987) 202 [INSPIRE].
G.W. Gibbons, M.J. Perry and C.N. Pope, Partition functions, the Bekenstein bound and temperature inversion in anti-de Sitter space and its conformal boundary, Phys. Rev.D 74 (2006) 084009 [hep-th/0606186] [INSPIRE].
F. Bonetti, T.W. Grimm and S. Hohenegger, One-loop Chern-Simons terms in five dimensions, JHEP07 (2013) 043 [arXiv:1302.2918] [INSPIRE].
T.W. Grimm, H. het Lam, K. Mayer and S. Vandoren, Four-dimensional black hole entropy from F-theory, JHEP01 (2019) 037 [arXiv:1808.05228] [INSPIRE].
C. Vafa, Instantons on D-branes, Nucl. Phys.B 463 (1996) 435 [hep-th/9512078] [INSPIRE].
A. Strominger, Black hole entropy from near horizon microstates, JHEP02 (1998) 009 [hep-th/9712251] [INSPIRE].
J. de Boer, Six-dimensional supergravity on S 3×AdS 3and 2D conformal field theory, Nucl. Phys.B 548 (1999) 139 [hep-th/9806104] [INSPIRE].
J. de Boer, Large N elliptic genus and AdS/CFT correspondence, JHEP05 (1999) 017 [hep-th/9812240] [INSPIRE].
E. Witten, On the conformal field theory of the Higgs branch, JHEP07 (1997) 003 [hep-th/9707093] [INSPIRE].
O. Ohlsson Sax, A. Sfondrini and B. Stefanski, Integrability and the conformal field theory of the Higgs branch, JHEP06 (2015) 103 [arXiv:1411.3676] [INSPIRE].
J.R. David, G. Mandal and S.R. Wadia, Microscopic formulation of black holes in string theory, Phys. Rept.369 (2002) 549 [hep-th/0203048] [INSPIRE].
J.M. Maldacena, G.W. Moore and A. Strominger, Counting BPS black holes in toroidal type II string theory, hep-th/9903163 [INSPIRE].
L. Eberhardt, M.R. Gaberdiel and W. Li, A holographic dual for string theory on AdS 3 × S 3 × S 3 × S 1, JHEP08 (2017) 111 [arXiv:1707.02705] [INSPIRE].
S. Gukov, E. Martinec, G.W. Moore and A. Strominger, The search for a holographic dual to AdS 3 × S 3 × S 3 × S 1, Adv. Theor. Math. Phys.9 (2005) 435 [hep-th/0403090] [INSPIRE].
D. Tong, The holographic dual of AdS 3 × S 3 × S 3 × S 1, JHEP04 (2014) 193 [arXiv:1402.5135] [INSPIRE].
J.M. Maldacena, A. Strominger and E. Witten, Black hole entropy in M-theory, JHEP12 (1997) 002 [hep-th/9711053] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].
P. Kraus and F. Larsen, Partition functions and elliptic genera from supergravity, JHEP01 (2007) 002 [hep-th/0607138] [INSPIRE].
L. Eberhardt, Supersymmetric AdS 3supergravity backgrounds and holography, JHEP02 (2018) 087 [arXiv:1710.09826] [INSPIRE].
S. Datta, L. Eberhardt and M.R. Gaberdiel, Stringy N = (2, 2) holography for AdS 3, JHEP01 (2018) 146 [arXiv:1709.06393] [INSPIRE].
B. Haghighat, S. Murthy, C. Vafa and S. Vandoren, F-theory, spinning black holes and multi-string branches, JHEP01 (2016) 009 [arXiv:1509.00455] [INSPIRE].
C. Couzens, C. Lawrie, D. Martelli, S. Schäfer-Nameki and J.-M. Wong, F-theory and AdS 3/CFT 2, JHEP08 (2017) 043 [arXiv:1705.04679] [INSPIRE].
C. Couzens, D. Martelli and S. Schäfer-Nameki, F-theory and AdS 3/CFT 2 (2, 0), JHEP06 (2018) 008 [arXiv:1712.07631] [INSPIRE].
L. Eberhardt, private communication.
A. Arabi Ardehali, High-temperature asymptotics of supersymmetric partition functions, JHEP07 (2016) 025 [arXiv:1512.03376] [INSPIRE].
T. Hartman, C.A. Keller and B. Stoica, Universal spectrum of 2d conformal field theory in the large c limit, JHEP09 (2014) 118 [arXiv:1405.5137] [INSPIRE].
N. Benjamin, M.C.N. Cheng, S. Kachru, G.W. Moore and N.M. Paquette, Elliptic genera and 3d gravity, Annales Henri Poincaré 17 (2016) 2623 [arXiv:1503.04800] [INSPIRE].
J.L. Cardy, Operator content and modular properties of higher dimensional conformal field theories, Nucl. Phys.B 366 (1991) 403 [INSPIRE].
A. Arabi Ardehali, High-temperature asymptotics of the 4d superconformal index, Ph.D. thesis, Michigan U., Ann Arbor, MI, U.S.A. (2016) [arXiv:1605.06100] [INSPIRE].
H.-B. Zhang and X. Zhang, One loop partition function from normal modes for N = 1 supergravity in AdS 3, Class. Quant. Grav.29 (2012) 145013 [arXiv:1205.3681] [INSPIRE].
I.V. Tyutin and M.A. Vasiliev, Lagrangian formulation of irreducible massive fields of arbitrary spin in (2 + 1)-dimensions, Theor. Math. Phys.113 (1997) 1244 [Teor. Mat. Fiz.113N1 (1997) 45] [hep-th/9704132] [INSPIRE].
A.N. Redlich, Gauge noninvariance and parity violation of three-dimensional fermions, Phys. Rev. Lett.52 (1984) 18 [INSPIRE].
A.N. Redlich, Parity violation and gauge noninvariance of the effective gauge field action in three-dimensions, Phys. Rev.D 29 (1984) 2366 [INSPIRE].
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Ardehali, A.A., Larsen, F., Liu, J.T. et al. Quantum corrections to central charges and supersymmetric Casimir energy in AdS3/CFT2. J. High Energ. Phys. 2019, 71 (2019). https://doi.org/10.1007/JHEP07(2019)071
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DOI: https://doi.org/10.1007/JHEP07(2019)071